Scarf coming in one's mouth while fasting

Q: Frequently, when going in sajdah, the fabric of my headscarf or the prayer mat ends up on my lips or in my mouth. This is an issue when I’m fasting. I don’t know if anything like microfibers or small hairs have entered my mouth. Today this happened during salah but I couldn’t feel anything in my mouth after it occurred so I assumed I could swallow as usual.

1. Was this correct?

2. If this happens during salah, and I feel something in my mouth after, do I have to spit?

3. If this happens in salah or near the end of it, do I have to check in a mirror afterwards to see if anything inside my mouth?

Changing one's intention of staying away from sins

Q: I made a niyat a few months ago and now I want to make some changes to it because it is getting difficult to stick to the niyat. I made a niyat like this that "I am making niyat that I will stop committing this sin from today"

My question is, while making niyat I did not take Allah Ta'ala's name, I just said that I am making this niyat and is it still necessary for me to stick to this niyat? I want to stay on this but I just want to make some changes in it.

Omitting Surah Faatihah in the third or fourth rakaat

Q:

1. During the fardh salaah of Zohr, Asr, Maghrib and Isha, can the imam omit Surah Fatiha in the 3rd/4th rakat (when there is time constraints)? Stand for 3 subhanallahs before going in ruku.

2. Also, when one is performing Salah individually can one omit for the same reasons?

3. What is the status of Surah Fatiha in 3rd and 4th rakaat? i.e. Fardh, wajib, mustahab etc.

4. Is there any hadeeth to support?